Theorems · Theorem · functional analysis
nnnorm_pow
∀ {α : Type u_2} [inst : SeminormedRing α] [NormOneClass α] [NormMulClass α] (a : α) (n : ℕ), ‖a ^ n‖₊ = ‖a‖₊ ^ n- Defined in
- Mathlib.Analysis.Normed.Ring.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NNRealstatement · cited by 4,310
- NNNorm.nnnormstatement · cited by 952
- SeminormedRingstatement and proof · cited by 446
- NormOneClassstatement and proof · cited by 136
- NormMulClassstatement and proof · cited by 66
- MonoidWithZeroHom.toMonoidHomproof · cited by 39
- MonoidHom.map_powproof · cited by 30
- nnnormHomproof · cited by 7
Cited by8
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
- Complex.nnnorm_eq_one_of_pow_eq_oneproof · cited by 1
- spectrum.spectralRadius_le_pow_nnnorm_pow_one_divproof · cited by 1
- enorm_powproof · cited by 1
- spectrum.spectralRadius_pow_leproof · cited by 1
- ModularFormClass.exists_boundproof · cited by 1
- ProbabilityTheory.evariance_def'proof · cited by 0
- Polynomial.IsRoot.norm_lt_cauchyBoundproof · cited by 0